This project is mainly devoted to applications of diffusion and random walk theory to biological and chemical phenomena. A singular perturbation theory has been developed to study diffusion in a force field when diffusive effects are small relative to the force. The general theory has application to chromatographic and electrophoretic processes as well as to chemical models which include potential barriers. A second project is the development of a mathematical model for optical imaging of highly absorbing regions in slablike media. A random walk model which has successfully been applied to other optical imaging problems can be adapted for use in this situation and has been shown to provide easily computable results that characterize the detection power inherent in transillumination measurements.